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Journal of Control Science and Engineering
Volume 2017, Article ID 3949428, 8 pages
https://doi.org/10.1155/2017/3949428
Research Article

Synchronization of Coupled Harmonic Oscillators Using Quantized Sampled Position Data

The School of Resources and Environment, North China University of Water Resource and Electric Power, Zhengzhou 450045, China

Correspondence should be addressed to Xinjing Wang; moc.361@888gnijnixgnaw

Received 27 February 2017; Revised 25 April 2017; Accepted 29 May 2017; Published 3 July 2017

Academic Editor: Wenwu Yu

Copyright © 2017 Xinjing Wang and Peipei He. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. H. Su, X. Wang, and Z. Lin, “Synchronization of coupled harmonic oscillators in a dynamic proximity network,” Automatica, vol. 45, no. 10, pp. 2286–2291, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  2. J. Zhou, H. Zhang, L. Xiang, and Q. Wu, “Sampled-data synchronization of coupled harmonic oscillators with controller failure and communication delays,” Theoretical and Applied Mechanics Letters, vol. 3, no. 6, Article ID 063002, 2013. View at Publisher · View at Google Scholar
  3. W. Ren, “Synchronization of coupled harmonic oscillators with local interaction,” Automatica, vol. 44, no. 12, pp. 3195–3200, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  4. X. Wang and Z. Cheng, “Synchronization of coupled discrete-time harmonic oscillators with rational frequency,” Institute of Electrical and Electronics Engineers. Transactions on Automatic Control, vol. 58, no. 6, pp. 1573–1579, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. J. Wang, J. Feng, C. Xu, M. Z. Q. Chen, Y. Zhao, and J. Feng, “The synchronization of instantaneously coupled harmonic oscillators using sampled data with measurement noise,” Automatica, vol. 66, pp. 155–162, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  6. J. Zhou, H. Zhang, L. Xiang, and Q. Wu, “Synchronization of coupled harmonic oscillators with local instantaneous interaction,” Automatica, vol. 48, no. 8, pp. 1715–1721, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  7. H. Zhang and J. Zhou, “Synchronization of sampled-data coupled harmonic oscillators with control inputs missing,” Systems & Control Letters, vol. 61, no. 12, pp. 1277–1285, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  8. Q. Song, W. Yu, J. Cao, and F. Liu, “Reaching Synchronization in Networked Harmonic Oscillators with Outdated Position Data,” IEEE Transactions on Cybernetics, vol. 46, no. 7, pp. 1566–1578, 2016. View at Publisher · View at Google Scholar · View at Scopus
  9. Q. Song, F. Liu, G. Wen, J. Cao, and Y. Tang, “Synchronization of coupled harmonic oscillators via sampled position data control,” IEEE Transactions on Circuits and Systems. I. Regular Papers, vol. 63, no. 7, pp. 1079–1088, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. T. Zhang and J. Li, “Robust iterative learning control of multi-agent systems with logarithmic quantizer,” in Proceedings of the 34th Chinese Control Conference, CCC 2015, pp. 7033–7038, chn, July 2015. View at Publisher · View at Google Scholar · View at Scopus
  11. S. R. Etesami and T. Başar, “Convergence Time for Unbiased Quantized Consensus over Static and Dynamic Networks,” IEEE Transactions on Automatic Control, vol. 61, no. 2, pp. 443–455, 2016. View at Publisher · View at Google Scholar · View at Scopus
  12. X. Guo, J. Wang, F. Liao, and D. Wang, “Quantized H∞ consensus of multi-Agent systems with quantization mismatch under switching weighted topologies,” IEEE Transactions on Control of Network Systems, vol. PP, no. 99, 2015. View at Publisher · View at Google Scholar · View at Scopus
  13. Z. Qiu, L. Xie, and Y. Hong, “Quantized leaderless and leader-following consensus of high-order multi-agent systems with limited data rate,” Institute of Electrical and Electronics Engineers. Transactions on Automatic Control, vol. 61, no. 9, pp. 2432–2447, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. Y. Zhu, Y. Zheng, and L. Wang, “Quantised consensus of heterogeneous multi-agent systems,” IET Control Theory & Applications, vol. 9, no. 17, pp. 2553–2560, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  15. S. Zhu and B. Chen, “Quantized consensus by the {ADMM}: probabilistic versus deterministic quantizers,” IEEE Transactions on Signal Processing, vol. 64, no. 7, pp. 1700–1713, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. Z. Zhang, L. Zhang, F. Hao, and L. Wang, “Periodic Event-Triggered Consensus with Quantization,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 63, no. 4, pp. 406–410, 2016. View at Publisher · View at Google Scholar · View at Scopus
  17. M. El Chamie, J. Liu, and T. Basar, “Design and analysis of distributed averaging with quantized communication,” Institute of Electrical and Electronics Engineers. Transactions on Automatic Control, vol. 61, no. 12, pp. 3870–3884, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  18. W. Xiong, X. Yu, Y. Chen, and J. Gao, “Quantized Iterative Learning Consensus Tracking of Digital Networks With Limited Information Communication,” IEEE Transactions on Neural Networks and Learning Systems, 2016. View at Publisher · View at Google Scholar · View at Scopus
  19. T. Basar, S. R. Etesami, and A. Olshevsky, “Convergence time of quantized Metropolis consensus over time-varying networks,” Institute of Electrical and Electronics Engineers. Transactions on Automatic Control, vol. 61, no. 12, pp. 4048–4054, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  20. X. Mu and K. Liu, “Containment control of single-integrator network with limited communication data rate,” Institute of Electrical and Electronics Engineers. Transactions on Automatic Control, vol. 61, no. 8, pp. 2232–2238, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. L. Rong, H. Shen, and J. Li, “Distributed quantised consensus in groups of agents with acceleration-like inputs: a reference model-based scheme,” IET Control Theory & Applications, vol. 10, no. 5, pp. 590–598, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  22. Z. Zhang, L. Zhang, F. Hao, and L. Wang, “Leader-Following consensus for linear and lipschitz nonlinear multiagent systems with quantized communication,” IEEE Transactions on Cybernetics, 2016. View at Publisher · View at Google Scholar · View at Scopus
  23. Z. Zeng, X. Wang, Z. Zheng, and L. Zhao, “Edge agreement of second-order multi-agent system with dynamic quantization via the directed edge Laplacian,” Nonlinear Analysis. Hybrid Systems, vol. 23, pp. 1–10, 2017. View at Publisher · View at Google Scholar · View at MathSciNet
  24. H.-X. Hu, Q. Xuan, W. Yu, C.-G. Zhang, and G. Xie, “Second-order consensus for heterogeneous multi-agent systems in the cooperation-competition network: a hybrid adaptive and pinning control approach,” Nonlinear Analysis. Hybrid Systems, vol. 20, pp. 21–36, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  25. H.-X. Hu, W. Yu, G. Wen, Q. Xuan, and J. Cao, “Reverse group consensus of multi-agent systems in the cooperation-competition network,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 63, no. 11, pp. 2036–2047, 2016. View at Publisher · View at Google Scholar · View at Scopus
  26. N. Elia and S. K. Mitter, “Stabilization of linear systems with limited information,” Institute of Electrical and Electronics Engineers. Transactions on Automatic Control, vol. 46, no. 9, pp. 1384–1400, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  27. M. Fu and L. Xie, “The sector bound approach to quantized feedback control,” Institute of Electrical and Electronics Engineers. Transactions on Automatic Control, vol. 50, no. 11, pp. 1698–1711, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  28. W. Ren and R. W. Beard, “Consensus seeking in multiagent systems under dynamically changing interaction topologies,” Institute of Electrical and Electronics Engineers. Transactions on Automatic Control, vol. 50, no. 5, pp. 655–661, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  29. P. C. Parks and V. Hahn, Stability Theory, Qrentice-Hall, NY, USA, 1993.